This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332307 #12 Feb 16 2025 08:33:59 %S A332307 1,1,1,1,4,1,1,8,8,1,1,14,20,14,1,1,22,62,62,22,1,1,32,132,276,132,32, %T A332307 1,1,44,336,1006,1006,336,44,1,1,58,688,3610,4324,3610,688,58,1,1,74, %U A332307 1578,12010,26996,26996,12010,1578,74,1,1,92,3190,38984,109722,229348,109722,38984,3190,92,1 %N A332307 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph. %H A332307 Andrew Howroyd, <a href="/A332307/b332307.txt">Table of n, a(n) for n = 1..435</a> %H A332307 J. L. Jacobsen, <a href="http://dx.doi.org/10.1088/1751-8113/40/49/003">Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions</a>, J. Phys. A: Math. Theor. 40 (2007) 14667-14678. %H A332307 J.-M. Mayer, C. Guez and J. Dayantis, <a href="http://dx.doi.org/10.1103/PhysRevB.42.660">Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices</a>, Physical Review B, Vol. 42 Number 1, 1990. %H A332307 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a> %H A332307 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a> %F A332307 T(n,m) = T(m,n). %e A332307 Array begins: %e A332307 ================================================ %e A332307 m\n | 1 2 3 4 5 6 7 %e A332307 ----+------------------------------------------- %e A332307 1 | 1 1 1 1 1 1 1 ... %e A332307 2 | 1 4 8 14 22 32 44 ... %e A332307 3 | 1 8 20 62 132 336 688 ... %e A332307 4 | 1 14 62 276 1006 3610 12010 ... %e A332307 5 | 1 22 132 1006 4324 26996 109722 ... %e A332307 6 | 1 32 336 3610 26996 229348 1620034 ... %e A332307 7 | 1 44 688 12010 109722 1620034 13535280 ... %e A332307 ... %Y A332307 Rows n=1..9 are A000012, A003682, A003685, A003695, A003778, A145402, A358794, A358795, A358796. %Y A332307 Main diagonal is A120443. %Y A332307 Cf. A064298, A231829, A271465, A271592, A288518, A321172. %K A332307 nonn,tabl %O A332307 1,5 %A A332307 _Andrew Howroyd_, Feb 09 2020